Please explain to me how to do these problems...Thanks
1. Find the value of x...x/6-x/8=1
2. The combined resistance of two resistors r1 and r2 in a parallel circuit is given by the formula
rt= 1/(1/r1)+ (1/r2)...simplify the formula...
3. Fungicides account for 1/10 of the pesticides used in the US. Insecticides account for 1/4 of all the pesticides in the US. The ratio of fungicides to insecticides used in the US can be written 1/10 divided by 1/4, write this ratio in simplest form...
1) is the common denominator 24?
2) is the common denominator (1/r1r2)?
3) Hmmm. Fungicides are not pesticides. However, ignoring that, follow the instructions in the problem. Show some work.
there is no common denominator on either problem, I am needing help to come up with the answer..
For 3, convert to decimals to get a better idea of the ratio — .10 and .25.
I hope this helps a little more. Thanks for asking.
Sure! I'll explain how to solve each problem step-by-step:
1. Find the value of x:
To solve this equation, we'll first find a common denominator for the fractions on the left side. You correctly suggested using 24 as the common denominator. Let's proceed with that:
x/6 - x/8 = 1
To convert the fractions to have a common denominator of 24, multiply the numerator and denominator of the first fraction (x/6) by 4, and the second fraction (x/8) by 3:
(4/4)(x/6) - (3/3)(x/8) = 1
4x/24 - 3x/24 = 1
Now that the fractions have the same denominator, we can combine the numerators:
(4x - 3x)/24 = 1
Simplify the numerator:
x/24 = 1
To solve for x, multiply both sides of the equation by 24 to cancel out the denominator:
x = 24
Therefore, the value of x is 24.
2. Simplify the formula for combined resistance:
The formula for combined resistance in a parallel circuit is given by:
rt = 1/(1/r1) + (1/r2)
To simplify this formula, we'll take the reciprocal of each term. The reciprocal of a fraction a/b is b/a. Applying this to our formula, we get:
rt = 1/(1/r1) + 1/(1/r2)
To find the common denominator, we can use the product of r1 and r2, which is r1 * r2. Writing the fractions with the common denominator, we have:
rt = r2/(r2/r1) + r1/(r1/r2)
Simplifying further, we have:
rt = r2 * (r1/r2r1) + r1 * (r2/r1r2)
Cancel out the common denominators, and simplify:
rt = r1 + r2
Therefore, the simplified formula for combined resistance in a parallel circuit is rt = r1 + r2.
3. Simplify the ratio of fungicides to insecticides:
The ratio of fungicides to insecticides used in the US can be written as 1/10 divided by 1/4.
To divide fractions, we'll multiply the first fraction by the reciprocal of the second fraction:
(1/10) ÷ (1/4) = (1/10) * (4/1)
Multiply the numerators and denominators:
4/10
Simplify the fraction by canceling out common factors:
4/10 = 2/5
Therefore, the ratio of fungicides to insecticides used in the US, written in simplest form, is 2/5.
I hope this explanation helps! Let me know if you have any further questions.